437 research outputs found

### Supersymmetry and superalgebra for the two-body system with a Dirac oscillator interaction

Some years ago, one of the authors~(MM) revived a concept to which he gave
the name of single-particle Dirac oscillator, while another~(CQ) showed that it
corresponds to a realization of supersymmetric quantum mechanics. The Dirac
oscillator in its one- and many-body versions has had a great number of
applications. Recently, it included the analytic expression for the eigenstates
and eigenvalues of a two-particle system with a new type of Dirac oscillator
interaction of frequency~$\omega$. By considering the latter together with its
partner corresponding to the replacement of~$\omega$ by~$-\omega$, we are able
to get a supersymmetric formulation of the problem and find the superalgebra
that explains its degeneracy.Comment: 21 pages, LaTeX, 1 figure (can be obtained from the authors), to
appear in J. Phys.

### Mass spectra of the particle-antiparticle system with a Dirac oscillator interaction

The present view about the structure of mesons is that they are a quark-antiquark system. The mass spectrum corresponding to this system should, in principle, be given by chromodynamics, but this turns out to be a complex affair. Thus it is of some interest to consider relativistic systems of particle-antiparticle, with a simple type of interaction, which could give some insight on the spectra we can expect for mesons. This analysis is carried out when the interaction is of the Dirac oscillator type. It is shown that the Dirac equation of the antiparticle can be obtained from that of the particle by just changing the frequency omega into -omega. Following a procedure suggested by Barut, the equation for the particle-antiparticle system is derived and it is solved by a perturbation procedure. Thus, explicit expressions for the square of the mass spectra are obtained and its implications in the meson case is discussed

### Playing relativistic billiards beyond graphene

The possibility of using hexagonal structures in general and graphene in
particular to emulate the Dirac equation is the basis of our considerations. We
show that Dirac oscillators with or without restmass can be emulated by
distorting a tight binding model on a hexagonal structure. In a quest to make a
toy model for such relativistic equations we first show that a hexagonal
lattice of attractive potential wells would be a good candidate. First we
consider the corresponding one-dimensional model giving rise to a
one-dimensional Dirac oscillator, and then construct explicitly the
deformations needed in the two-dimensional case. Finally we discuss, how such a
model can be implemented as an electromagnetic billiard using arrays of
dielectric resonators between two conducting plates that ensure evanescent
modes outside the resonators for transversal electric modes, and describe an
appropriate experimental setup.Comment: 23 pages, 8 figures. Submitted to NJ

### Survival and Nonescape Probabilities for Resonant and Nonresonant Decay

In this paper we study the time evolution of the decay process for a particle
confined initially in a finite region of space, extending our analysis given
recently (Phys. Rev. Lett. 74, 337 (1995)). For this purpose, we solve exactly
the time-dependent Schroedinger equation for a finite-range potential. We
calculate and compare two quantities: (i) the survival probability S(t), i.e.,
the probability that the particle is in the initial state after a time t; and
(ii) the nonescape probability P(t), i.e., the probability that the particle
remains confined inside the potential region after a time t. We analyze in
detail the resonant and nonresonant decay. In the former case, after a very
short time, S(t) and P(t) decay exponentially, but for very long times they
decay as a power law, albeit with different exponents. For the nonresonant case
we obtain that both quantities differ initially. However, independently of the
resonant and nonresonant character of the initial state we always find a
transition to the ground state of the system which indicates a process of
``loss of memory'' in the decay.Comment: 26 pages, RevTex file, figures available upon request from
[email protected] (To be published in Annals of Physics

### Relativistic echo dynamics and the stability of a beam of Landau electrons

We extend the concepts of echo dynamics and fidelity decay to relativistic
quantum mechanics, specifically in the context of Klein-Gordon and Dirac
equations under external electromagnetic fields. In both cases we define
similar expressions for the fidelity amplitude under perturbations of these
fields, and a covariant version of the echo operator. Transformation properties
under the Lorentz group are established. An alternate expression for fidelity
is given in the Dirac case in terms of a 4-current. As an application we study
a beam of Landau electrons perturbed by field inhomogeneities.Comment: 8 pages, no figure

### Classifying Reported and "Missing" Resonances According to Their P and C Properties

The Hilbert space H^3q of the three quarks with one excited quark is
decomposed into Lorentz group representations. It is shown that the quantum
numbers of the reported and ``missing'' resonances fall apart and populate
distinct representations that differ by their parity or/and charge conjugation
properties. In this way, reported and ``missing'' resonances become
distinguishable. For example, resonances from the full listing reported by the
Particle Data Group are accommodated by Rarita-Schwinger (RS) type
representations (k/2,k/2)*[(1/2,0)+(0,1/2)] with k=1,3, and 5, the highest spin
states being J=3/2^-, 7/2^+, and 11/2^+, respectively. In contrast to this,
most of the ``missing'' resonances fall into the opposite parity RS fields of
highest-spins 5/2^-, 5/2^+, and 9/2^+, respectively. Rarita-Schwinger fields
with physical resonances as lower-spin components can be treated as a whole
without imposing auxiliary conditions on them. Such fields do not suffer the
Velo-Zwanziger problem but propagate causally in the presence of
electromagnetic fields. The pathologies associated with RS fields arise
basically because of the attempt to use them to describe isolated spin-J=k+1/ 2
states, rather than multispin-parity clusters. The positions of the observed RS
clusters and their spacing are well explained trough the interplay between the
rotational-like (k/2)(k/2 +1)-rule and a Balmer-like -(k+1)^{-2}-behavior

### The no-core shell model with general radial bases

Calculations in the ab initio no-core shell model (NCSM) have conventionally
been carried out using the harmonic-oscillator many-body basis. However, the
rapid falloff (Gaussian asymptotics) of the oscillator functions at large
radius makes them poorly suited for the description of the asymptotic
properties of the nuclear wavefunction. We establish the foundations for
carrying out no-core configuration interaction (NCCI) calculations using a
basis built from general radial functions and discuss some of the
considerations which enter into using such a basis. In particular, we consider
the Coulomb-Sturmian basis, which provides a complete set of functions with a
realistic (exponential) radial falloff.Comment: 7 pages, 3 figures; presented at Horizons on Innovative Theories,
Experiments, and Supercomputing in Nuclear Physics 2012, New Orleans,
Louisiana, June 4-7, 2012; submitted to J. Phys. Conf. Se

### The Dirac Oscillator. A relativistic version of the Jaynes--Cummings model

The dynamics of wave packets in a relativistic Dirac oscillator is compared
to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the
Dirac oscillator produces the entanglement of the spin with the orbital motion
similar to what is observed in the model of quantum optics. The collapses and
revivals of the spin which result extend to a relativistic theory our previous
findings on nonrelativistic oscillator where they were known under the name of
`spin-orbit pendulum'. There are important relativistic effects (lack of
periodicity, zitterbewegung, negative energy states). Many of them disappear
after a Foldy-Wouthuysen transformation.Comment: LaTeX2e, uses IOP style files (included), 14 pages, 9 separate
postscript figure

### Quantum-wave evolution in a step potential barrier

By using an exact solution to the time-dependent Schr\"{o}dinger equation
with a point source initial condition, we investigate both the time and spatial
dependence of quantum waves in a step potential barrier. We find that for a
source with energy below the barrier height, and for distances larger than the
penetration length, the probability density exhibits a {\it forerunner}
associated with a non-tunneling process, which propagates in space at exactly
the semiclassical group velocity. We show that the time of arrival of the
maximum of the {\it forerunner} at a given fixed position inside the potential
is exactly the traversal time, $\tau$. We also show that the spatial evolution
of this transient pulse exhibits an invariant behavior under a rescaling
process. This analytic property is used to characterize the evolution of the
{\it forerunner}, and to analyze the role played by the time of arrival,
$3^{-1/2}\tau$, found recently by Muga and B\"{u}ttiker [Phys. Rev. A {\bf 62},
023808 (2000)].Comment: To be published in Phys. Rev. A (2002

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